Contracting cubeΒΆ
In this demo we simulate a unit cube that is fixed at \(x = 0\) and free at \(x = 1\). We use a transversally isotropic material with fiber oriented in the \(x\)-direction.
import dolfin
try:
from dolfin_adjoint import (
Constant,
DirichletBC,
Expression,
UnitCubeMesh,
interpolate,
Mesh,
)
except ImportError:
from dolfin import (
Constant,
DirichletBC,
interpolate,
Expression,
UnitCubeMesh,
Mesh,
)
import pulse
from fenics_plotly import plot
pulse.iterate.logger.setLevel(10)
# Create mesh
N = 6
mesh = UnitCubeMesh(N, N, N)
# Create subdomains
class Free(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] > (1.0 - dolfin.DOLFIN_EPS) and on_boundary
class Fixed(dolfin.SubDomain):
def inside(self, x, on_boundary):
return x[0] < dolfin.DOLFIN_EPS and on_boundary
# Create a facet fuction in order to mark the subdomains
ffun = dolfin.MeshFunction("size_t", mesh, 2)
ffun.set_all(0)
# Mark the first subdomain with value 1
fixed = Fixed()
fixed_marker = 1
fixed.mark(ffun, fixed_marker)
# Mark the second subdomain with value 2
free = Free()
free_marker = 2
free.mark(ffun, free_marker)
# Create a cell function (but we are not using it)
cfun = dolfin.MeshFunction("size_t", mesh, 3)
cfun.set_all(0)
# Collect the functions containing the markers
marker_functions = pulse.MarkerFunctions(ffun=ffun, cfun=cfun)
# Create mictrotructure
V_f = dolfin.VectorFunctionSpace(mesh, "CG", 1)
# Fibers
f0 = interpolate(Expression(("1.0", "0.0", "0.0"), degree=1), V_f)
# Sheets
s0 = interpolate(Expression(("0.0", "1.0", "0.0"), degree=1), V_f)
# Fiber-sheet normal
n0 = interpolate(Expression(("0.0", "0.0", "1.0"), degree=1), V_f)
# Collect the mictrotructure
microstructure = pulse.Microstructure(f0=f0, s0=s0, n0=n0)
# Create the geometry
geometry = pulse.Geometry(
mesh=mesh,
marker_functions=marker_functions,
microstructure=microstructure,
)
# Use the default material parameters
material_parameters = pulse.HolzapfelOgden.default_parameters()
# Select model for active contraction
active_model = pulse.ActiveModels.active_strain
# active_model = "active_stress"
# Set the activation
activation = Constant(0.0)
# Create material
material = pulse.HolzapfelOgden(
active_model=active_model,
parameters=material_parameters,
activation=activation,
)
# Make Dirichlet boundary conditions
def dirichlet_bc(W):
V = W if W.sub(0).num_sub_spaces() == 0 else W.sub(0)
return DirichletBC(V, Constant((0.0, 0.0, 0.0)), fixed)
# Make Neumann boundary conditions
neumann_bc = pulse.NeumannBC(traction=Constant(0.0), marker=free_marker)
# Collect Boundary Conditions
bcs = pulse.BoundaryConditions(dirichlet=(dirichlet_bc,), neumann=(neumann_bc,))
# Create problem
problem = pulse.MechanicsProblem(geometry, material, bcs)
# Solve problem
pulse.iterate.iterate(problem, activation, 0.1)
2021-11-23 16:53:55,769 [792] DEBUG pulse.iterate: Control: [0.0]
2021-11-23 16:53:55,771 [792] DEBUG pulse.iterate: Target: [0.1]
2021-11-23 16:53:55,772 [792] DEBUG pulse.iterate: Intial number of steps: 5 with step size 0.02
2021-11-23 16:53:55,773 [792] INFO pulse.iterate: Iterating to target control (f_21)...
2021-11-23 16:53:55,773 [792] INFO pulse.iterate: Current control: f_21 = 0.000
2021-11-23 16:53:55,774 [792] INFO pulse.iterate: Target: 0.100
2021-11-23 16:53:55,779 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:53:55,781 [792] DEBUG pulse.iterate: Maximum difference: 1.000e-01
2021-11-23 16:53:55,782 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:53:55,783 [792] DEBUG pulse.iterate: Current control: 0.020
2021-11-23 16:53:57,625 [792] DEBUG pulse.iterate: Solver did not converge...
2021-11-23 16:53:57,626 [792] DEBUG pulse.iterate:
NOT CONVERGING
2021-11-23 16:53:57,627 [792] DEBUG pulse.iterate: Reduce control step
2021-11-23 16:53:57,628 [792] DEBUG pulse.iterate: Assign old state
2021-11-23 16:53:57,636 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:53:57,637 [792] DEBUG pulse.iterate: Maximum difference: 1.000e-01
2021-11-23 16:53:57,637 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:53:57,638 [792] DEBUG pulse.iterate: Current control: 0.010
2021-11-23 16:54:03,289 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:03,290 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:03,291 [792] DEBUG pulse.iterate: Maximum difference: 9.000e-02
2021-11-23 16:54:03,292 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:03,293 [792] DEBUG pulse.iterate: Maximum difference: 9.000e-02
2021-11-23 16:54:03,294 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:03,294 [792] DEBUG pulse.iterate: Current control: 0.020
2021-11-23 16:54:05,704 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:05,705 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:05,706 [792] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2021-11-23 16:54:05,708 [792] DEBUG pulse.iterate: Adapt step size. New step size: 0.015
2021-11-23 16:54:05,709 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:05,710 [792] DEBUG pulse.iterate: Maximum difference: 8.000e-02
2021-11-23 16:54:05,711 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:05,712 [792] DEBUG pulse.iterate: Current control: 0.035
2021-11-23 16:54:09,056 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:09,057 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:09,058 [792] DEBUG pulse.iterate: Maximum difference: 6.500e-02
2021-11-23 16:54:09,059 [792] DEBUG pulse.iterate: Adapt step size. New step size: 0.022
2021-11-23 16:54:09,061 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:09,061 [792] DEBUG pulse.iterate: Maximum difference: 6.500e-02
2021-11-23 16:54:09,062 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:09,064 [792] DEBUG pulse.iterate: Current control: 0.058
2021-11-23 16:54:11,955 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:11,956 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:11,957 [792] DEBUG pulse.iterate: Maximum difference: 4.250e-02
2021-11-23 16:54:11,957 [792] DEBUG pulse.iterate: Adapt step size. New step size: 0.034
2021-11-23 16:54:11,958 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:11,959 [792] DEBUG pulse.iterate: Maximum difference: 4.250e-02
2021-11-23 16:54:11,960 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:11,962 [792] DEBUG pulse.iterate: Current control: 0.091
2021-11-23 16:54:13,414 [792] DEBUG pulse.iterate: Solver did not converge...
2021-11-23 16:54:13,415 [792] DEBUG pulse.iterate:
NOT CONVERGING
2021-11-23 16:54:13,415 [792] DEBUG pulse.iterate: Reduce control step
2021-11-23 16:54:13,416 [792] DEBUG pulse.iterate: Assign old state
2021-11-23 16:54:13,425 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:13,425 [792] DEBUG pulse.iterate: Maximum difference: 4.250e-02
2021-11-23 16:54:13,427 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:13,428 [792] DEBUG pulse.iterate: Current control: 0.074
2021-11-23 16:54:16,260 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:16,261 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:16,262 [792] DEBUG pulse.iterate: Maximum difference: 2.563e-02
2021-11-23 16:54:16,263 [792] DEBUG pulse.iterate: Adapt step size. New step size: 0.025
2021-11-23 16:54:16,265 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:16,266 [792] DEBUG pulse.iterate: Maximum difference: 2.563e-02
2021-11-23 16:54:16,267 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:16,268 [792] DEBUG pulse.iterate: Current control: 0.100
2021-11-23 16:54:17,728 [792] DEBUG pulse.iterate: Solver did not converge...
2021-11-23 16:54:17,729 [792] DEBUG pulse.iterate:
NOT CONVERGING
2021-11-23 16:54:17,730 [792] DEBUG pulse.iterate: Reduce control step
2021-11-23 16:54:17,730 [792] DEBUG pulse.iterate: Assign old state
2021-11-23 16:54:17,738 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:17,738 [792] DEBUG pulse.iterate: Maximum difference: 2.563e-02
2021-11-23 16:54:17,739 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:17,740 [792] DEBUG pulse.iterate: Current control: 0.087
2021-11-23 16:54:20,073 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:20,074 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:20,075 [792] DEBUG pulse.iterate: Maximum difference: 1.297e-02
2021-11-23 16:54:20,076 [792] DEBUG pulse.iterate: Adapt step size. New step size: 0.019
2021-11-23 16:54:20,077 [792] DEBUG pulse.iterate: Check target reached: NO
2021-11-23 16:54:20,079 [792] DEBUG pulse.iterate: Maximum difference: 1.297e-02
2021-11-23 16:54:20,080 [792] DEBUG pulse.iterate: Change step size for final iteration
2021-11-23 16:54:20,081 [792] DEBUG pulse.iterate: Try new control
2021-11-23 16:54:20,081 [792] DEBUG pulse.iterate: Current control: 0.100
2021-11-23 16:54:22,013 [792] DEBUG pulse.iterate:
SUCCESFULL STEP:
2021-11-23 16:54:22,014 [792] DEBUG pulse.iterate: Check target reached: YES!
2021-11-23 16:54:22,015 [792] DEBUG pulse.iterate: Check target reached: YES!
([Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 47),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 195),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 246),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 313),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 372),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 466),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 552),
Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', tetrahedron, 1), dim=3), 0), MixedElement(VectorElement(FiniteElement('Lagrange', tetrahedron, 2), dim=3), FiniteElement('Lagrange', tetrahedron, 1))), 595)],
[Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 45),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 193),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 244),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 311),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 370),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 464),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 550),
Coefficient(FunctionSpace(None, FiniteElement('Real', None, 0)), 593)])
# Get displacement and hydrostatic pressure
u, p = problem.state.split(deepcopy=True)
V = dolfin.VectorFunctionSpace(mesh, "CG", 1)
u_int = interpolate(u, V)
new_mesh = Mesh(mesh)
dolfin.ALE.move(new_mesh, u_int)
fig = plot(mesh, show=False)
fig.add_plot(plot(new_mesh, color="red", show=False))
fig.show()